Articles publicats en revistes (Matemàtiques i Informàtica)

Permanent URI for this collectionhttps://hdl.handle.net/2445/7508

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Gaussian lower bound and positivity of the density of stochastic delay differential equations driven by a fractional Brownian motion
(Sveučilište Josipa Jurja Strossmayera u Osijeku, 2026-04-02) Burés Mogollón, Òscar; Rovira Escofet, Carles
In this paper, we prove that the density of a stochastic delay differential equation driven by a fBm with Hurst parameter > 1/2 is strictly positive combining Nourdin-Viens’ and Kohatsu-Higa’s method.
Closure properties of measurable ultrapowers
(Association for Symbolic Logic., 2021-05-06) Lücke, Philipp; Müller, Sandra
We study closure properties of measurable ultrapowers with respect to Hamkin’s notion of freshness and show that the extent of these properties highly depends on the combinatorial properties of the underlying model of set theory. In one direction, a result of Sakai shows that, by collapsing a strongly compact cardinal to become the double successor of a measurable cardinal, it is possible to obtain a model of set theory in which such ultrapowers possess the strongest possible closure properties. In the other direction, we use various square principles to show that measurable ultrapowers of canonical inner models only possess the minimal amount of closure properties. In addition, the techniques developed in the proofs of these results also allow us to derive statements about the consistency strength of the existence of measurable ultrapowers with non-minimal closure properties.
The basepoint-freeness threshold of a very general abelian surface
(Springer Nature, 2022-01-07) Rojas González, Andrés
For abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepoint-freeness threshold. Our main tool is the relation between cohomological rank functions and Bridgeland stability. In virtue of recent results of Caucci and Ito, these computations provide new information on the syzygies of polarized abelian surfaces.
Convex analysis on polyhedral spaces
(Springer Verlag, 2022-01-24) Botero, Ana María; Burgos Gil, José I.; Sombra, Martín
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
Steel’s Programme: Evidential Framework, the Core and Ultimate-L
(Association for Symbolic Logic., 2023) Bagaria, Joan; Ternullo, Claudio
We address Steel’s Programme to identify a ‘preferred’ universe of set theory and the best axioms extending ZFC by using his multiverse axioms MV and the ‘core hypothesis’. In the first part, we examine the evidential framework for MV, in particular the use of large cardinals and of ‘worlds’ obtained through forcing to ‘represent’ alternative extensions of ZFC. In the second part, we address the existence and the possible features of the core of MVT (where T is ZFC+Large Cardinals). In the last part, we discuss the hypothesis that the core is Ultimate-L, and examine whether and how, based on this fact, the Core Universist can justify V=Ultimate-L as the best (and ultimate) extension of ZFC. To this end, we take into account several strategies, and assess their prospects in the light of MV’s evidential framework.
Invariant manifolds near L1 and L2 in the Sun–Jupiter elliptic restricted three-body problem I
(Springer Verlag, 2024-08-01) Duarte, Gladston; Jorba i Monte, Àngel
In this paper, we present a way of combining the computation of invariant tori and their stable and unstable manifolds with the multiple shooting technique. We start by showing some of the results of Jorba (Nonlinearity 14(5):943–976, 2001) that should be modified in order to introduce the multiple shooting technique in these computations. After that, by a direct application in the planar elliptic restricted three-body problem (PERTBP), how to modify the equations and methods to compute the above-mentioned objects is introduced. In particular, the structure of the (systems of) equations and matrices involved in these computations is shown. An application of these computations can be found in Duarte and Jorba (Invariant manifolds of tori near and in the planar elliptic restricted three-body problem II. The Dynamics of Comet Oterma, Preprint 2023), where the dynamics of comet 39P/Oterma is modelled as a PERTBP.
Invariant manifolds near L1 and L2 in the Sun–Jupiter elliptic restricted three-body problem II: the dynamics of comet Oterma
(Springer Verlag, 2024-12-01) Duarte, Gladston; Jorba i Monte, Àngel
Comet 39P/Oterma is known to make fast transitions between heliocentric orbits outside the orbit of Jupiter and heliocentric orbits inside that of Jupiter. In this paper, the dynamics of comet Oterma is modelled and fitted in the Planar Elliptic RTBP. Using the computations presented in Duarte(Celest. Mech. Dyn. Astron 136:26, 2024), we look for the invariant objects around and , which in the case of the Planar Elliptic RTBP is invariant tori and their stable and unstable manifolds that are the skeleton that guides Oterma in its rapid transition.
Semiconvexity estimates for nonlinear integro-differential equations
(Wiley, 2025-03-01) Ros, Xavier; Torres Latorre, Clara; Weidner, Marvin
In this paper we establish for the first time local semiconvexity estimates for fully nonlinear equations and for obstacle problems driven by integro-differential operators with general kernels. Our proof is based on the Bernstein technique, which we develop for a natural class of nonlocal operators and consider to be of independent interest. In particular, we solve an open problem from Cabré-Dipierro-Valdinoci. As an application of our result, we establish optimal regularity estimates and smoothness of the free boundary near regular points for the nonlocal obstacle problem on domains. Finally, we also extend the Bernstein technique to parabolic equations and nonsymmetric operators.
Tent Carleson measures for Hardy spaces
(Elsevier, 2024-07-15) Lv, Xiaofen; Pau, Jordi
We completely characterize those positive Borel measures $\mu$ on the unit ball $\mathbb{B}_n$ such that the Carleson embedding from Hardy spaces $H^p$ into the tent-type spaces $T_s^q(\mu)$ is bounded, for all possible values of $0<p, q, s<\infty$.
Well-posedness and inverse problems for semilinear nonlocal wave equations
(Elsevier, 2024-10-01) Lin, Yi-Hsuan; Tyni, Teemu; Zimmermann, Philipp
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main challenge is due to the low regularity of the solutions of linear nonlocal wave equations. We then turn to an inverse problem of recovering the nonlinearity of the equation. More precisely, we show that the exterior Dirichlet-to-Neumann map uniquely determines homogeneous nonlinearities of the form $f(x, u)$ under certain growth conditions. On the other hand, we also prove that initial data can be determined by using passive measurements under certain nonlinearity conditions. The main tools used for the inverse problem are the unique continuation principle of the fractional Laplacian and a Runge approximation property. The results hold for any spatial dimension $n \in \mathbb{N}$.
Quantum geometric-entropic optimization for customer lifetime value prediction: convergence theory and an empirical study on transactional retail data
(Taylor & Francis, 2026-05-11) Ferrara, Massimiliano; Sáez Ortuño, Laura; Forgas Coll, Santiago; Fabila-Fabián, Jorge Refugio; Martín Isla, Carlos; Lekadir, Karim, 1977-
Predicting customer churn from transactional data is a central problem in management science, with direct implications for retention strategy, revenue forecasting, and resource allocation. This paper introduces Quantum Geometric-Entropic Optimization (Q-GEO), a framework that integrates Geometric-Entropic Optimization – combining Riemannian gradient methods with entropy-regularized optimal transport – into the training of variational quantum kernels for classification. The algorithm operates on a parameter manifold equipped with a Fisher-Wasserstein metric and incorporates Sinkhorn-type projections to enforce distributional coherence on the quantum feature space. We establish three theoretical contributions: (i) a convergence theorem for Q-GEO-trained variational quantum kernels under a combined Polyak–Łojasiewicz and Sinkhorn contraction framework, yielding linear convergence in the Riemannian condition number plus geometric contraction of the Sinkhorn residual; (ii) a margin amplification result showing that GEO-trained quantum embeddings achieve improved separation bounds over Euclidean-trained counterparts due to the spectral regularization provided by the Wasserstein component of the Fisher-Wasserstein metric; and (iii) a distributional stability result proving that Sinkhorn-projected quantum kernel matrices preserve a doubly stochastic spectral structure that mitigates kernel collapse in imbalanced settings. We validate the framework on the UCI Online Retail II dataset ( =5,942 customers, d=11 RFM-extended features, churn rate ≈37%), a publicly available transactional benchmark. Under nested cross-validation, Q-GEO achieves 0.8614 accuracy, 0.8103 precision, 0.7891 recall, 0.7996 F1, and 0.9047 ROC AUC, outperforming both classical baselines (including logistic regression, random forest, XGBoost, and CatBoost) and standard variational quantum kernel methods. We complement the accuracy analysis with SHAP-based explainability, computation time comparisons, and a detailed feature engineering appendix to support interpretability and reproducibility. We interpret these results as evidence that geometric optimization principles can materially enhance quantum machine learning for management science applications.
Lattice path matroids and quotients
(Springer Verlag, 2024-04-04) Benedetti Velásquez, Carolina; Knauer, Kolja
We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams. This characterization allows us to show that ordering LPMs by quotients yields a graded poset, whose rank polynomial has the Narayana numbers as coefficients. Furthermore, we study full lattice path flag matroids and show that—contrary to arbitrary positroid flag matroids—they correspond to points in the nonnegative flag variety. At the basis of this result lies an identification of certain intervals of the strong Bruhat order with lattice path flag matroids. A recent conjecture of Mcalmon, Oh, and Xiang states a characterization of quotients of positroids. We use our results to prove this conjecture in the case of LPMs.
Lagrangian Subspaces of the Moduli Space of Simple Sheaves on K3 Surfaces
(Springer Verlag, 2025-01-04) Fantechi, Barbara; Miró-Roig, Rosa M. (Rosa Maria)
Let $X$ be a K3 surface and let $\operatorname{Spl}\left(r ; c_1, c_2\right)$ be the moduli space of simple sheaves on $X$ of fixed rank $r$ and Chern classes $c_1$ and $c_2$. Under suitable assumptions, to a pair ( $F, W$ ) (respectively, $(F, V)$ ) where $F \in \operatorname{Spl}\left(r ; c_1, c_2\right)$ and $W \subset H^0(F)$ (resp. $V^* \subset H^1\left(F^*\right)$ ) is a vector subspace, we associate a simple syzygy bundle (resp. extension bundle) on $X$. We show that both syzygy bundles and extension bundles can be constructed in families and that the induced morphism to a different component of the moduli of simple sheaves is a locally closed embedding. We show that this construction associates with every Lagrangian (resp. isotropic) algebraic subspace of $\operatorname{Spl}\left(r ; c_1, c_2\right)$ an induced Lagrangian (resp. isotropic) algebraic subspace of a different component of the moduli of simple sheaves.
Continuity of the j-function on the Markov tree
(London Mathematical Society, 2024-11-01) Bengoechea, Paloma
One way of defining the values of the modular $j$-function at real quadratic irrationalities is by its cycle integrals along geodesics in the upper half plane whose endpoints are the roots of an indefinite binary quadratic form. We show that the restriction of the modular $j$-function to Markov irrationalities (an important subset of real quadratic irrationalities in diophantine approximation) is continuous with respect to the topology induced by the
Reflecting measures
(Elsevier B.V., 2024-05-01) Bagaria, Joan; Goldberg, Gabriel
We give new, purely combinatorial characterizations of several kinds of large cardinals, such as strongly $C^{(n)}$-compact and $C^{(n)}$-extendible, in terms of reflecting measures. We then study the key property of tightness of elementary embeddings that witness strong $C^{(n)}$-compactness, which prompts the introduction of the new large-cardinal notion of tightly $C^{(n)}$-compact cardinal. Then we prove, assuming the Ultrapower Axiom, that a cardinal is tightly $C^{(n)}$-compact if and only if it is either $C^{(n-1)}$-extendible or a measurable limit of $C^{(n-1)}$-extendible cardinals. In the last section we also give new characterizations of $\Sigma_n$-strong cardinals in terms of reflecting extenders.
Weight decompositions on algebraic models for mapping spaces and homotopy automorphisms
(Springer Verlag, 2024-07-11) Cirici, Joana; Saleh, Bashar
We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components of holomorphic maps between compact Kähler manifolds as well as homotopy automorphisms of Kähler manifolds.
Weighted Strong-Type Estimates on Classical Lorentz Spaces
(Springer Verlag, 2024-01-20) Baena Miret, Sergi
We present new estimates in the setting of weighted classical Lorentz spaces for important operators in Harmonic Analysis such as Calderón-Zygmund operators, sparse operators and the Bochner-Riesz operator among others.
Superelliptic curves with large Galois images
(Springer Verlag, 2025-02-07) Goodman, Pip
Let $r>2$ and $\ell$ be primes. In this paper we study the $\bmod \ell$ Galois representations attached to curves of the form $y^r=f(x)$ where $f$ is monic and has coefficients belonging to the $r$ th cyclotomic field. We provide conditions on the coefficients (and degree) of $f$ which allow one to verify the $\bmod \ell$ image is large outside of a (typically small) finite explicit set of primes. We allow all values of $r$ for which the $r$ th cyclotomic field has odd class number. This appears to be the first explicit result for abelian varieties of dimension greater than two and not of $\mathrm{GL}_2$-type which allows the ground field to have unramified extensions. To determine the exact image we study the "endomorphism character", a certain algebraic Hecke character which generalises the CM character. This is achieved in entirety when $r=3$. To the author's knowledge, this is the first accurate description of the full image in the literature. Finally, we give several examples with genus ranging from 10 to 36. Applications to the Inverse Galois Problem are also included.
Parabolic Boundary Harnack Inequalities with Right-Hand Side
(Springer Verlag, 2024-08-26) Torres Latorre, Clara
We prove the parabolic boundary Harnack inequality in parabolic flat Lipschitz domains by blow-up techniques, allowing, for the first time, a non-zero right-hand side. Our method allows us to treat solutions to equations driven by non-divergence form operators with bounded measurable coefficients, and a right-hand side $f \in L^q$ for $q>n+2$. In the case of the heat equation, we also show the optimal $C^{1-\varepsilon}$ regularity of the quotient. As a corollary, we obtain a new way to prove that flat Lipschitz free boundaries are $C^{1, \alpha}$ in the parabolic obstacle problem and in the parabolic Signorini problem.
AI-augmented pathology: the experience of transfer learning and intra-domain data diversity in breast cancer metastasis detection
(Frontiers Media, 2025-06-11) Cossio, Manuel; Wiedemann, Nina; Sanfeliu Torres, Esther; Barnadas Sole, Ester; Igual Muñoz, Laura
Background: Metastatic detection in sentinel lymph nodes remains a crucial prognostic factor in breast cancer management, with accurate and timely diagnosis directly impacting treatment decisions. While traditional histopathological assessment relies on microscopic examination of stained tissues, the digitization of slides as whole-slide images (WSI) has enabled the development of computer-aided diagnostic systems. These automated approaches offer potential improvements in detection consistency and efficiency compared to conventional methods. Results: This study leverages transfer learning on hematoxylin and eosin (HE) WSIs to achieve computationally efficient metastasis detection without compromising accuracy. We propose an approach for generating segmentation masks by transferring spatial annotations from immunohistochemistry (IHC) WSIs to corresponding H&E slides. Using these masks, four distinct datasets were constructed to fine-tune a pretrained ResNet50 model across eight different configurations, incorporating varied dataset combinations and data augmentation techniques. To enhance interpretability, we developed a visualization tool that employs color-coded probability maps to highlight tumor regions alongside their prediction confidence. Our experiments demonstrated that integrating an external dataset (Camelyon16) during training significantly improved model performance, surpassing the benefits of data augmentation alone. The optimal model, trained on both external and local data, achieved an accuracy and F1-score of 0.98, outperforming existing state-of-the-art methods. Conclusions: This study demonstrates that transfer learning architectures, when enhanced with multi-source data integration and interpretability frameworks, can significantly improve metastatic detection in whole slide imaging. Our methodology achieves diagnostic performance comparable to gold-standard techniques while dramatically accelerating analytical workflows. The synergistic combination of external dataset incorporation and probabilistic visualization outputs provides a clinically actionable solution that maintains both computational efficiency and pathological interpretability.

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